Rigidity of free product von Neumann algebras

Cyril Houdayer, Yoshimichi Ueda

研究成果: ジャーナルへの寄稿記事

6 引用 (Scopus)

抄録

Let be any nonempty set and (M i , φi)i∈I let be any family of nonamenable factors, endowed with arbitrary faithful normal states, that belong to a large class C anti-free of (possibly type ) von Neumann algebras including all nonprime factors, all nonfull factors and all factors possessing Cartan subalgebras. For the free product (M , φ) =i∈I (M i φi), we show that the free product von Neumann algebra M retains the cardinality [I] and each nonamenable factor M i up to stably inner conjugacy, after permutation of the indices. Our main theorem unifies all previous Kurosh-type rigidity results for free product type II 1 factors and is new for free product type III factors. It moreover provides new rigidity phenomena for type III factors.

元の言語英語
ページ(範囲)2461-2492
ページ数32
ジャーナルCompositio Mathematica
152
発行部数12
DOI
出版物ステータス出版済み - 12 1 2016

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Free Product
Von Neumann Algebra
Rigidity
Cartan Subalgebra
Conjugacy
Faithful
Cardinality
Permutation
Arbitrary
Theorem

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

これを引用

Rigidity of free product von Neumann algebras. / Houdayer, Cyril; Ueda, Yoshimichi.

:: Compositio Mathematica, 巻 152, 番号 12, 01.12.2016, p. 2461-2492.

研究成果: ジャーナルへの寄稿記事

Houdayer, Cyril ; Ueda, Yoshimichi. / Rigidity of free product von Neumann algebras. :: Compositio Mathematica. 2016 ; 巻 152, 番号 12. pp. 2461-2492.
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